A collision in Phystown is being analyzed by the O.P.P. accident analysis team. A 1000 kg Toyota known to be moving at 65 km/h [W] collided at an intersection with a 3000 kg SUV moving [N]. After the collision, the two vehicles "stuck" together and the police estimate that immediately after impact the Toyota-SUV wreckage moved at 45 km/h. Based on this information, what was the speed of the SUV before the collision?
initial momentum=final momentum
notice this is a vector equation, so you have to work it in N and W directions.
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To determine the speed of the SUV before the collision, we need to apply the principles of conservation of momentum.
First, let's convert the given speeds to meters per second (m/s) for consistency:
65 km/h * (1000 m/km) / (3600 s/hr) ≈ 18.06 m/s (Toyota's initial speed)
45 km/h * (1000 m/km) / (3600 s/hr) ≈ 12.5 m/s (Speed after the collision)
Next, we need to set up an equation using the conservation of momentum principle:
Initial momentum = Final momentum
The initial momentum is the sum of the momenta of the two vehicles before the collision, and the final momentum is the momentum of the combined wreckage after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v): p = mv.
Let's denote the initial velocity of the SUV as vX, and the initial velocity of the Toyota as vY.
The initial momentum before the collision is given by:
(3000 kg * vX) + (1000 kg * vY)
The final momentum after the collision is given by:
(4000 kg * 12.5 m/s)
According to the conservation of momentum principle, the initial momentum equals the final momentum:
(3000 kg * vX) + (1000 kg * vY) = (4000 kg * 12.5 m/s)
Now we can solve for vX, the initial velocity of the SUV:
3000 kg * vX = (4000 kg * 12.5 m/s) - (1000 kg * vY)
3000 kg * vX = 50,000 kg * m/s - 1000 kg * vY
vX ≈ (50,000 kg * m/s - 1000 kg * vY) / 3000 kg
However, we need more information about the collision, specifically the direction of the SUV's motion. If the SUV was heading north as stated, we can determine its speed.
Since the SUV is moving north, its velocity can be represented as vY.
vY ≈ (50,000 kg * m/s - 3000 kg * vX) / 1000 kg
By substituting the given values into the equation and solving for vY, we can determine the speed of the SUV before the collision.